The USS Enterprise is trying to fix extreme weather problems resulting from an asteroid collision on the planetPenthara IV, a colony with a population of some twenty million persons. On their way to Penthara IV, Worf notices a space-time distortion, followed by the appearance of a small vessel. CaptainPicard tries to hail the ship, to which the occupant replies that Picard should move over. Picard takes a stand saying that the Enterprise will not go anywhere until it explains itself. As soon as Picard physically "moves over," a man named Berlinghoff Rasmussen appears aboard the Enterprise claiming to be a historian from the future (specifically, the 26th century), specializing in 24th century interstellar issues.

Rasmussen tries to convince the crew that he is actually from the future. In order to prove it, the crew tries asking him questions that only a man from the future would know the answers to. DoctorCrusher wants to know if they cured the Telurian plague by Rasmussen's time, but Picard says they shouldn't ask questions like that, despite the temptation. After the meeting is over, Deanna Troi says Rasmussen is holding something back, but is unsure that it has to do with his wanting to keep information from his century from the crew of the Enterprise.

Rasmussen tries to study Data in a turbolift while he escorts him to his newly assigned quarters. Data tries to ask about whether or not he lives to see the 26th century, but Rasmussen avoids his questions and tells him that it would be better if Data kept those assumptions to himself. Data complies, apologizes, and leaves Rasmussen alone. After Data leaves, Rasmussen looks around his quarters with a sinister expression on his face.

"Captain's Log: Stardate 45350.3. We have arrived at Penthara IV and can see for ourselves the atmospheric devastation caused by the asteroid's impact."

The Enterprise arrives at Penthara IV. Meanwhile, in Ten Forward, Riker, Worf, and Crusher are talking about Rasmussen's presence while sitting at a table. His presence on board is quite disruptive since he refuses to reveal anything about the future, but he nevertheless drops many hints that something important is about to happen. Rasmussen arrives in Ten Forward and Dr. Crusher invites him to the group's table. He asks them to each take a questionnaire. Then they talk about how they view the world and what they each think the most important inventions/advancements in the past 200 years were. Beverly says the way surgery was changed, Riker says warp coils, and Worf says phasers. Rasmussen says that it's typical that they would provide such different answers since Beverly is a doctor, Riker is a commander in Starfleet, and Worf is from a warrior background. Later, Rasmussen visits Geordi La Forge and Data in Engineering. La Forge conjectures that Rasmussen is there to witness the mission at Penthara IV after he comments on how little is known of Data's part in the mission in the 26th century. La Forge figures out the parameters of how much CO2 to inject into the air at Penthara IV and tells Picard he is ready to transport to the planet's surface. When La Forge leaves, Rasmussen steals a PADD left on the table. He then goes to the bridge to witness the event.

Troi and Crusher are in sickbay discussing if Rasmussen is really just after historical facts or more. Rasmussen comes into sickbay and Troi tries to excuse herself but he manages to talk about how she doesn't trust him, but she does finally leave. Rasmussen makes a pass at Beverly by telling her she has been the only person to make him think about not returning to where he is from. Beverly deters him by saying she could very well be his great-great-great-great-grandmother. Rasmussen leaves sickbay with a neural stimulator.

Meanwhile, the initial attempt to release carbon dioxide from inside the planet into the atmosphere was briefly successful, but unanticipated volcanic activity released more particulates into the atmosphere, making the problem worse.

Rasmussen goes to Data's quarters and finds him listening to 4 pieces of music loudly and Rasmussen is confused as to how he can listen to all that simultaneously. Data replies that he is capable of distinguishing over 150 simultaneous compositions from each other. Then La Forge sends a transmission to Data from the surface of the planet, and while they are discussing if Data made any errors, Rasmussen pockets a tricorder from Data's room. Data then notifies Picard in his ready room that they have already done everything they can, and if they try again and err, they would completely burn off the planet's atmosphere.

"Captain's Log, supplemental. While Doctor Moseley takes La Forge's plan to the leaders of the colony I find myself weighing the potential consequences of a more philosophical issue."

"Captain's Log: Stardate 45351.9. Doctor Moseley has met with the colony leaders who all agree they are willing to take the risk."

On the planet, Doctor Moseley and La Forge are trying to work out new parameters to stop the planet from freezing over or burning up the atmosphere. Rasmussen is called by Picard into his ready room because he faces a dilemma of how to help the Pentharians.

The Enterprise initiates a reaction

The Enterprise can initiate a chain reaction in the atmosphere that should fix the problem, but if calculations are ever so slightly off, life on the planet will be wiped out. Picard forcefully asks for Rasmussen's help: can he tell what happened to Penthara IV? While Picard concedes that there might be some sort of Temporal Prime Directive in the future that precludes Rasmussen from aiding him, he argues that this is certainly a situation where the directive could be violated. Picard also theorizes that since Rasmussen's past is Picard's own future, choosing to try is the right thing to do. Rasmussen refuses to help and Picard ultimately chooses not to play it safe and decides to try and save the planet.

The Enterprise prepares to discharge an immense amount of energy from the deflector dish using an auto-phaser interlock. La Forge and Data's plan is that the phaser energy will ionize the particles in Penthara IV's atmosphere, eliminating the electrostatic energy and returning the planet's ecosystem back to normal. The plan is set in motion and everything goes well, with the Enterprise sending the resulting energy that shoots out from the planet into open space. Dr. Moseley and La Forge report that the particulate levels are where they are supposed to be and that Penthara's sun is shining through.

Meanwhile, a number of small objects have been found missing and Picard suspects Rasmussen. He nods to Worf right after Rasmussen makes a hasty departure from the bridge after Penthara IV has been saved. Later, Rasmussen is confronted by Picard, Riker, Crusher, Worf, Data, and Garvey in one of the Enterprise's shuttlebays shortly before he heads back into the future. Rasmussen asks to let Data inspect his time-travel pod for the missing items, Picard reasoning that Data is the only person who can be definitely trusted not to divulge about anything he witnessed inside the pod. Once inside, Rasmussen attempts to abduct Data and reveals that he is indeed from 200 years outside the Enterprise's timeframe, but in the opposite direction – he is actually from New Jersey on Earth in the 22nd century. He stole the time-travel pod from the original time traveler from the future, and he plans to return to his own time with the high-tech objects he has stolen, now including Data, and "invent" them. However, his attempt is foiled, as the stolen phaser he planned to use to knock out Data has been deactivated remotely via a signal they transmitted into the pod when the door was open. Inside, Data postulates that the handprint lock will probably work whether Rasmussen is "conscious or not." They step back out into the shuttlebay and once Worf retrieves the stolen items Picard orders him to arrest Rasmussen, despite his pleas to be let go. The pod vanishes, stranding him in the future. Worf leads Rasmussen to the brig, with Picard welcoming him to the 24th century and remarking there are "many legitimate historians that would be interested in talking to a Human from your era."

"To try or not to try. To take a risk or play it safe. Your arguments have reminded me how precious the right to choose is. And because I've never been one to play it safe, I choose to try."

- Jean-Luc Picard

"I assume your handprint will open this door whether you are conscious or not."

- Data, in a subtle threat to subdue Rasmussen after his phaser fails to fire

"I'm sure there are more than a few legitimate historians at Starfleet who would be eager to meet a human from your era. Oh, Professor! Welcome to the 24th century."

- Jean-Luc Picard, to Rasmussen

"Yes, Professor, I know. What if one of those lives I save down there is a child who grows up to be the next Adolf Hitler or Khan Singh? Every first year philosophy student has been asked that question since the earliest wormholes were discovered..."

Rick Berman commented, "I am fascinated by all the episodes that have dealt with the implausibility of time travel. I have always had in my head the idea of an episode that had someone who was capable of time travel and professes he is from the future, and we find out he is actually from the past. It's part of that Mark Twain feeling of what Leonardo da Vinci could have done with a calculator or Alexander the Great with a shotgun." (Captains' Logs: The Unauthorized Complete Trek Voyages)

Regarding the episode's tech subplot Berman recalled, "To sit with the scene guys and research and develop it and to try and come up with with something that would work, you get lost in the technical elements of it. You need other people to come and hit you over the head and pull it back. Sometimes we succeed with that and sometimes we don't." (Captains' Logs: The Unauthorized Complete Trek Voyages)

There is a reference to this episode in the Star Trek: Deep Space Ninefourth season episode "Bar Association". In that episode, Odo cites the case of Rasmussen as an example of a security breach aboard the Enterprise. Miles O'Brien also mentions this incident in the novel Inferno after the universe is destroyed in 2400 as a result of the Bajoran wormhole meeting and consuming a red wormhole created by the Pah-wraiths, citing his encounter with 26th-century technology as a means of proving to his current 'crew' – consisting of Quark, Rom, Odo, and Garak – that it is possible for them to change history so that timelines where the universe didn't end in 2400 come into existence.

Rasmussen's question to Riker concerning what he thought was innovative about the USS Enterprise-B is the first canonical reference to that starship.

Michael Piller remarked, "Nobody ever just hands in a script – not me, not even Rick. It was a delightful change of pace and tone from the grimness and darkness of the Spock episode. It was just at the right time. Rick and I and the staff worked long and hard with him on the script and he had a lot of challenges to overcome. That fourth act where Picard and Ramussen have a one scene act is wonderful and I enjoyed that a lot." (Captains' Logs: The Unauthorized Complete Trek Voyages)

Director Paul Lynch stated, "It was more of a comedy than a drama. Matt Frewer was wonderful as a space con man... He got the reputation of being large for his comedy roles, but he was a consumate actor and he found the level of comedy and realism of the character which is what makes him such a good character. He was never schticky." (Captains' Logs: The Unauthorized Complete Trek Voyages)

In 2012, Paul Lynch stated that he felt "A Matter of Time" was his least favorite Star Trek: The Next Generation episode out of the five he had directed. [2]